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Boosting an old method with a new basis: MP2 electron correlation

Boosting an old method with a new basis: MP2 electron correlation. Andrea Sanfilippo, X.Ren, P. Rinke, V. Blum, K.Reuter, M. Scheffler. About me…. Andrea Sanfilippo. 2004 Degree in Material Science at the Milano-Bicocca University Thesis project :

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Boosting an old method with a new basis: MP2 electron correlation

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  1. Boosting an old method with a new basis: MP2 electron correlation Andrea Sanfilippo, X.Ren, P. Rinke, V. Blum, K.Reuter, M. Scheffler Fritz-Haber Institut der Max-Planck Gesellschaft

  2. About me… Andrea Sanfilippo 2004 Degree in Material Science at the Milano-Bicocca University Thesis project: Construction of an ab-initio Green function code for non-periodical systems using an Embedding Method (supervised by Trioni, Brivio) 2005/ 2006 Doctoral project at the University College of London: Hybrid computational method for scattering of elastic waves in Metal Matrix Composites Since January 2007 at the at Fritz-Haber Institut in Berlin: PhD on ab-initio study of Surface Molecular networks

  3. Introducing Electronic Structure Theory • Modern ab-initio methods in the Born-Oppenheimer approximation: • wave function (Hartree-Fock, post-HF, QM) • density functional methods (DFT) • Present day DFT functionals and wave function based methods treat accurately bonded systems like metals, semiconductors, molecules… • but…in nature weak interactions are widespread (physisorption, protein folding, glues etc.) How do we treat their ground states accurately and efficiently?

  4. DFT in brief , the Kohn-Sham trick ? • Exact Excunknow, is guessed (often parametrized) • local (TF, LDA): local density of homogenous and isotropic electron gas approximation • semi-local (GGAs): gradient expansions on LDA • non-local (OEP, HyFs, vdW): hybrid density/w.f. to recover long-range physical effects • There is not (yet) a systematic way to treat weak bonded systems • Computationally fast ~ O(N3), N number of basis E : Ground state energy, TS : Kinetic energy of the free electrons, VII : Nuclear interactions

  5. e- e- The grand-father method of quantum chemistry : Hartree-Fock (1930) • Hartree-Fock approximation • approximation: only Pauli principle considered, but it is a poor approximation, what is missing is called correlation • e- dig a hole around himself (like exact solution) : Fermi energy, V : Coulomb potential, n : density, VH Hartree potential

  6. Perturbation theory: MP2 (1934) • The second order of perturbation is a first estimation of correlation between two particles • Computation expensive ~ O(N5): terms • Basis set to expand MO: • Gaussian or Slater type basis set • Numerical Atomic Orbitals (NAO) • Gaussian generally used so far, to make it faster N : number of atomic basis functions, i,j : molecular orbitals label (spin included)

  7. Two basis set in comparison • Gaussian: • Localize basis set • Analytical integrals • Many functions required to recover physics • Construction problematic for heavier elements • Numerical atomic orbitals • Localized basis set • Numerical integration • Correct physics recovered few functions! • Can be more easily generated

  8. Aim of the project • Implementation of second order many body perturbation theory using numerical atomic orbital code using • Describe weak bonded systems efficiently with the highest accuracy • Applications: weak molecular bonds, extended systems in presence of heavy elements, surface physisorption

  9. To improve scaling and timing • Resolution of identity defined as projector giving a computationally cheaper term • In density fitting we introduce an auxiliary basis set the residual can be minimized depending on the metric. Vahtras, Almlof, Feyereiesen (1993) . Mulliken notation applied :

  10. Main Features of RI/DF-MP2 • Auxiliary basis set taken generally as m ~ N • Number of calculations ~ O(mN4), but computing time <10% than full-MP2 and storage can be reduced to ~ O(mN2) • RI-MP2 size consistent • Resulting error lower than the basis set error (error due to incompleteness of basis set, i.e. BSSE) Weigend et al. (2002) Weigend et al. (2002), Weigend (2006) , Sodt et al. (2006)

  11. What we have done so far… • RI-MP2 is feasible with NAO • Development of parallel RI-MP2 and BSSE correction using a NAO in-house code, “FHI-aims” • Basis set study starting from MP2 or DFT-LDA • Applied to small molecules and Hydrogen bonded system with accurate results further optimizations (matrix sparsity, PB …) and application to a wider range of practical systems, adsorption on surfaces in particular … and future The FHI Ab Initio Molecular Sim. (aims) project, www.fhiberlin.mpg.de/aims/

  12. Few examples… Water dimer (PBE optimized geometries) O2 NAO basis set applied here are LDA optimized

  13. Thanks! Aknowledgements: MONET - Molecular Networks at Phase Boundaries Marie Curie Early Stage Researcher Training Network The FHI Ab Initio Molecular Simulations (aims) project V. Blum and M. Scheffler; R. Gehrke, P. Havu, V. Havu, X. Ren, A. Sanfilippo, F. Hanke, A. Tkatchenko, P. Rinke, and K. Reuter. www.fhiberlin.mpg.de/aims/

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